Summary
- Periodic and quasi-periodic can help reveal properties of underlying object.
- Three methods for discovering periodicity: Lomb-Scargle periodogram (LSP), weighted wavelet Z-transform (WWZ), and Gaussian process regression
- Compare their results on two X-ray light curves from Swift that accompanied short gamma-ray bursts (sGRB).
- Found periodicity but needs to be confirmed
- Detrending was the biggest factor affecting the recovery of periods.
- Suggest X-rays originate from magnetar oscillations after binary merger or precession of newborn magnetar.
Data
- 124 sGRBs in third Swift-BAT catalogue (12/2004–07/2019)
- 67 BAT light curves with SNR > 3
- Chose 2 light curves with sufficient data:
- Used points from the initial WT (windowed timing) mode, not latter PC (photon counting) mode.
Data: sGRB 050724
Data: sGRB 060614
Methodology (Raw light curve)
- Fit GP
- Mean function: power law, polynomial.
- kernel: quasiperiodic, simple harmonic oscillator, damped random walk.
- Inspect hyperparameters
- period, P
- quality factor, Q > 0.5
Methodology (Detrending)
Detrend by subtracting from raw light curve
- Fitted GP
- Mean: power law, kernel: quasiperiodic.
- Mean: power law, kernel: damped random walk.
- Mean: polynomial, kernel: quasiperiodic.
- Mean: polynomial, kernel: simple harmonic oscillator.
- Mean: polynomial, kernel: damped random walk.
- Fitted polynomial
Methodology (Detrended light curve)
- Fit GP
- Mean function: constant.
- kernel: quasiperiodic, damped random walk.
- Calculate L-S periodogram
- Apply WWZ-transform
Results
Results
Results
Results
Conclusions
- Potential QPOs were detected.
- LSP, WWZ, and GPs seem consistent.
- Detrending has large influence, as does kernel and mean function.
Statistical nitpicking
- Detrending is like enforcing stationarity
- Detrending itself is not trivial; what order polynomial was used?
- equivalent to non-zero GP mean function
- Heavy selection bias (n = 2)
- Fitting Gaussian likelihood to X-ray data
- Using MLE to initialise MCMC is good practice
Hmmm…
![]()
![]()
Comments
celerite, could just cite.